Question

If a spring is stretched 4m from its starting length when 20n of force is applied, then how much work (in joules) is done by the spring when it is stretched 10 m?

Answer 1

ANSWER:

250 J

STEP-BY-STEP EXPLANATION:

F = 20N is required to stretch the spring by 4 meters

We know that the force is equal to:

$F=k\cdot x$

We solve for k (spring constant):

$k=\frac{F}{x}=\frac{20}{4}=5\text{ N/m}$

The work done in stretching the spring is given by the following equation (in this case the stretch is 10 meters:

$\begin{gathered} W=\frac{1}{2}k\cdot x^2 \\ \text{ Replacing} \\ W=\frac{1}{2}\cdot5\cdot10^2 \\ W=250\text{ J} \end{gathered}$

The work required is 250 joules.